Buoyancy Waves in Earth's Magnetosphere: Calculations for a 2-D Wedge Magnetosphere

To improve theoretical understanding of the braking oscillations observed in Earth's inner plasma sheet, we have derived a theoretical model that describes k(vertical bar vertical bar) = 0 magnetohydrodynamic waves in an idealized magnetospheric configuration that consists of a 2-D wedge with circular-arc field lines. The low-frequency, short-perpendicular-wavelength mode obeys a differential equation that is often used to describe buoyancy oscillations in a neutral atmosphere, so we call those waves "buoyancy waves," though the magnetospheric buoyancy force results from magnetic tension rather than gravity. Propagation of the wave is governed mainly by a position-dependent frequency omega(b), the "buoyancy frequency," which is a fundamental property of the magnetosphere. The waves propagate if omega(b) > omega but otherwise evanesce. In the wedge magnetosphere,omega(b) turns out to be exactly the fundamental oscillation frequency for poloidal oscillations of a thin magnetic filament, and we assume that the same is true for the real magnetosphere. Observable properties of buoyancy oscillations are discussed, but propagation characteristics vary considerably with the state of the magnetosphere. For a given event, the buoyancy frequency and propagation characteristics can be determined from pressure and density profiles and a magnetic field model, and these characteristics have been worked out for one typical configuration. A localized disturbance that initially resembles a dipolarizing flux bundle spreads east-west and also penetrates into the plasmasphere to some extent. The calculated amplitude near the center of the original wave packet decays in a few oscillation periods, even though our calculation includes no dissipation.